Algebraic equalities

An equation is an algebraic equality that is true only for some values of the variables. These values are called solutions of the equation.

An identity is an algebraic equality that is true for all values of the variables.

Example:

a + a = 2a is an identity

x + 7 = 9 is an equation. x = 2 is the solution

x + y = 5 is an equation.    x = 8 and y = -3 is a solution

Exercise: decide if the following equalities are equations or identities:

a) x + y + z = 28

b) x·(x+5) = x² +5x

c) x² - 5x + 4 = x² +25x

d) (x+1)² = x² + 2x +1

Solutions: a) equation; b) identity; c) equation; d) identity